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Probability

Probability

Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule about who will pay the bill: Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. Find the proba

Joint Probabilities Variables

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let T = Z / √ (V/n) Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)

Probability in Various Situations

Find the probability for the various situations 1. 5 individuals enter the ground floor of an elevator of a building which has 10 floors(9 floors above the ground floor). Assuming that each of the 5 individuals is going to depart the elevator on one of the 9 floors above the ground floor, (a) what is the probability that all

New Source, Inc. - Probability

NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource is considering following suit. Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to

Assigning Probabilities to simple events

When assigning probabilities of two simple events, can we assume that each event is always equally likely to occur and, thus assign .5 to each event? Could you provide an example in your explanation?

Difference Between the Quality of Care Provided

Saint Paul's Hospital commissioned an independent study to determine if there was a difference between the quality of care provided by hospital-trained nurses and tertiary-trained nurses. Two hundred nurses were rated as either providing Superior Service (S) or Adequate Service (A). The results are as follows: (See attached file

Probability - Orange dealership

The manager of an Orange dealership keeps records on customers visiting the store. Records show that 40% of the people visiting the store are female. Thirty-five percent (35%) of the females visiting the store will buy an Orange. The records also point out that 20% of the males visiting the store will buy an Orange. a) What i

This job calculates Probability.

A major hat store chain is having a sale on three nationally known brands, A, B and C. Probabilities that Brand A, Brand B or Brand C will not be big sellers are: 0.30, 0.40, and 0.50, respectively. All three brands are manufactured by three independent companies. Calculate the probability that: a. None of the brands will b

Probability is explained.

Two events, A and B are equally likely. The chance that either A or B happens on a given trial of an experiment is 0.70, while the chance that they both happen on a given trial is only 0.40. What is the probability that event A happens?

Normal and Poisson approximation to binomial distribution

In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365. For a given month find: 1) The probability taht

Normal & Poisson approximation to binomial distribution

A fair coin is tossed 100 times. The event that the number of heads obtained is less than 35 is denoted by A. By using a suitable approximation to the binomial distribution, calculate the probability of A. The event that A occurs more than 3 times when 2000 such coins are each tossed 100 times is denoted by B. By usin

Probability and Cumulative Distribution Function

1. A random variable X has the following cumulative distribution function F(x) = { 1 - e^(-(x+1)) -1</ x < oo 0 elsewhere. a) 25% of the time, X exceeds what value? b) Find the moment generating function of X, or Mx(t) c) Using your result in (b

Probability

The distribution of blood types for a population are: 40% typeA 9% type B 49% type O 2% type AB Suppose that the blood types are independent and that both the husband and the wife follow this distribution of blood type. a) If the wife has type B, what is the probability that the husband has type B? b) What is the pr

Probability

Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. What is the probability that the sample mean is less than 33?

Poisson vs. Gaussian distribution

Radiation: The atoms of a radioactive element are randomly disintegrating and emitting alpha particles. The number of alpha particles emitted per second from these atoms during a 30 second period is recorded as follows. 9.38 8.08 8.36 10.44 9.44 8.05 17.78 7.56 14.17 6.73 9.81 4.79 11.98 9.48 6.32 14.

Statistics - Probability Consumer Tastes

1) A record store owner wants to determine consumer tastes. She decides to observe customers in her store on a particular day and record the number of minutes the each spends in the Alternative Music and Rap sections of the store. She came up with the following data: Alternative Music Rap Mean = x = 25 Mean = 20 St

Mean, Standard Deviation & Probability Distribution

Find the mean, standard deviation and probability distribution for the given problems. 1. The average profit per unit for Product A is $5.32, Product B is $7.98, and Product C is $9.69. If the percentages of each sold are 36, 29, and 35 respectively, what is the weighted mean profit per unit? 2. A fleet of cabs fo

Probability and Expected Value

Find the expected profit in the given question. The Wilhelms Cola Company plans to market a new pineapple-flavored cola this summer. The decision is whether to package the cola in returnable or in no-return bottles. Currently, the state legislature is considering eliminating no-return bottles. Tybo Wilhelms, president of Wilh

Probability of Guessing Correctly

1. A committee consists of five Chicanos, two Asians, three African Americans, and two Caucasions. a) A subcommittee of four is chosen at random. What is the probability that all the ethnic groups are represented on the subcommittee? b) Answer the question for part (a) if a subcommittee of five is chosen. 2. The game of Ma

Statistics - polling

1. On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympics in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1011 adults, 18 years and older, conducted February 4 - 6, 2002.

Statistics: normally and binomially distributed random variables

1) A videotape store has an average weekly gross of $1,158 with a standard deviation of $120. Assuming this to be a normally distributed random variable, calculate the following: a. Probability the weekly gross will exceed $1,261. b. Proportion of weeks the weekly gross is less than $1,080. c. Probability the weekly gross is

Statistics problem

1) A survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had NOW accounts. Of those households with no checking account 40% had savings accounts. Of the households with regular checking accounts 71.6% had a savings account. Of the households with NOW accounts 7

Hamburger Probability of Incidents of People Becoming Ill

Because of a recent incident in which a number of people became ill after eating undercooked hamburger meat, intensive interest has centered around the cooking time for hamburger patties. In the past, the cooking time at a local fast food firm has been found to be uniformly distributed between 4 and 5 minutes. a) A TV report